ENGINEERINGREPORTS

The LocalizedSound PowerMethod*

EARL GEDDES AND HENRY BLIND

Diversified Products Technical Center, Electrical and Electronics Division, Ford Motor Company, Dearborn,MI 48121, USA

Single-point microphone measurements in enclosed spaces lack sufficient stabilityto be useful for sound system equalization (above the Schroeder frequency). A newmeasurement technique for use in automobiles was developed to circumvent this problem.The problems encountered with single-point measurements and the results obtainedwith the new system are described.

" 0 INTRODUCTION I THE SCHROEDER STATISTICS

Most sound system designers discover all too soon In 1954 Schroeder wrote the fundamental paper onthat designing flat sound system components does not statistical room theory [1]. This paper is must readingyield a satisfactory response once the system has been for anyone working in room acoustics. Schroeder showsinstalled in a room or enclosure. The total system re- that the pressure response in a room is essentially asponse will suffer from severe frequency response ab- random variable. As a simple example to demonstrateerrations due to the room's acoustical properties. From this principle, consider a room being excited by a purea systems standpoint, the listening space is the dominant tone emitted by a source. The room's response to thisfactor in the overall frequency response curve. Seldom, tone will depend upon the summation of the complexif ever, can we change the acoustic characteristics of pressures over all of the excited modes in the room.the listening space to correct for these undesirable fre- Each of these modes will contribute to the total sumquency response aberrations. It is for this reason that with a different amplitude and phase. Above thesound system equalization has become very popular as Schroeder frequency (where the eigenmodes are suf-a viable approach to correcting electrically what cannot ficiently dense) there will usually be hundreds of thesebe corrected acoustically. However, in order to take modes being excited by a pure tone. With this manythis approach one must know exactly what the room's virtually random (in phase and amplitude) modes beingfrequency response is before it can be corrected. This added together, the net summation will have a Gaussianreport will show that single-point microphone mea- distribution in both the real and the imaginary partssurements lack sufficient stability to be useful for sound (the central limit theorem). The net result will be ansystem equalization. A new measurement procedure amplitude response to the pure tone excitation whichwas developed which has proven to yield significantly must be dealt with as a random variable with a definedbetter results. Using this technique one can obtain a standard deviation. Stated more quantitatively [1]:

one-third-octave measurement of the acoustic frequency The frequency response curve of a "large room" willresponse with a 90% confidence of having no greater lie 70 percent of the time in a strip 11 dB wide about thethan a 0.5-dB expected error. This level of accuracy mean line. The only assumptions used were that the ei-is necessary for "unambiguous" sound system equal- genfrequencies are "sufficiently" dense and that the mi-ization, crophoneis placedsufficientlyfar fromthesoundsource

so as to be in the far field.* Presented at the 76th Convention of the Audio Engineering

Society, New York, 1984 October 8-11. Note that these assumptions are quite general. In

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GEDDES AND BLIND ENGINEERING REPORTS

essence they imply that the statistical properties of all of the measurement, the greater confidence one has inrooms are virtually identical above the Schroeder fre- the results. If a sufficient number of narrow-band mea-quency, about 50 Hz in a typical auditorium and 150 sures cannot be reasonably taken, then widening theto 200 Hz in an automobile. The Schroeder frequency bandwidth of the measurement is the only alternative.can be calculated from the equation [1] As a brief review, this section has shown the follow-

ing:F (Schroeder) = 2000V'T60/enclosure volume . 1) Single-point microphone measurements in enclosed

spaces lack sufficient stability to be useful for soundLet us look at this principle in another way: A single- equalization (within Schroeder's assumptions).

point microphone measurement has only a 70% con- 2) Any desired accuracy and confidence can be ob-fidence of obtaining a pressure response measurement rained by spatially averaging a wide-bandwidth signal.of a pure tone with an accuracy of better than 5.5 dB 3) The exact number of measurements and theirin any enclosure above its Schroeder frequency, bandwidth is hard to determine analytically and needsThis is hardly a stable enough measurement to allow to be done empirically.

one to equalize an audio system's sound pressure levelto within 1 dB or so. 2 TYPICAL EXAMPLE

Fig. 1 shows the effect on the expected error and In order to outline the approach one can take toconfidence interval for a pure-tone measurement as afunction of the number of statistically independent achieve the desired accuracy, consider a typical problemsamples. Notice that a 95% confidence of + 1.0-dB in sound system equalization. The first step is to measuremeasurement would require nearly 50 independent the frequency response of the present sound system.samples--an arduous task. An independent sample is Fig. 3 shows a typical one-third-octave response fromone whose position is spatially uncorrelated with another a real-time spectral analyzer of the response of a vehicleposition. This occurs when the two points are separated to a pink-noise input. The response clearly shows theneed for equalization. A serious question arises here:by at least a half-wavelength of the frequency being should this particular curve be equalized, that is, doesconsidered [2]. An absolute error of no greater than it accurately represent the true acoustic response of0.5 dB would probably not be obtainable for pure tonesat mid- to low frequencies, this enclosure? In light of our previous discussion theFig. 2 shows the effect of increasing the measurement answer to this question is no. Fig. 4 shows very clearly

bandwidth on the spatial variance of a sample. Increas- the lack of stability of a single-point measurement.This chart shows 18 different measurements of the sameing the bandwidth of the measurement has the effect vehicle plotted on a single axis. Each of these mca-of decreasing the expected error for spatially sampled surements was taken in a region within which theresignals. Thus by spatially sampling a number (to be was a 99% chance that a listener's ears would be located.determined) of one-third-octave measurements a + 0.5- Notice in this figure that many of these curves differdB measurement could be obtained. The exact effecton the spatial variance with bandwidth depends on the by more than 10 dB, even for the fairly wide one-third-octave bandwidth used in these measurements. Thereverberation time T60. The reverberation time is not effect of the location of the Schroeder frequency canalways known and not always easy to measure (as in be seen at about 150 Hz or so (no clear-cut transitiona vehicle). This problem makes it difficult to do an exists), below which the variation of the data showsexact error analysis for wide-bandwidth signals. Theimportant point here is that the wider the bandwidth significantly less deviation from curve to curve.

There are many considerations when attempting anexact error analysis of the equalization curve specifi-

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Fig. 1. Confidence limits for expected error as a function of Fig. 2. Spatial variance versus bandwidth of measurementthe number of independent samples. (for constant reverberation time)·

168 J. Audio Eng. Soc., Vol. 34, No. 3, 1986 March

ENGINEERING REPORTS LOCALIZED SOUND POWERMETHOD

cation. One needs to consider also the type of equalizer sound field measurements in automotive interiors. Theto be used (one-third-octave band, parametric, etc.), accuracy obtained with the procedure outlined herethe number of equalization bands, and the desired ac- will suit our needs at the present time and well intocuracy. All of these factors will help to determine the the foreseeable future.bandwidth of the measurement and the number of sam- One advantage that an automotive sound system de-ples required to obtain the goal. This presentation will signer has is that he or she always knows approximatelyshow one approach to obtaining very accurate and stable where the listener's head and ears will be. The people

Fig. 3. Typical one-third-octave in-car response curve for a single microphone position.

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Fig. 4. In-car response curves for 18 microphone measurements (within ear ellipse).

J. Audio Eng. Soc., Vol. 34, No. 3, 1988 March 169

GEDDESANDBLIND ENGINEERINGREPORTS

in our organization who are concerned with ergonomics often in relatively short time periods, required a re-have calculated the zone where 99% of the drivers' duction in the difficulty of the procedure. The physicaleyes will be located. These data are used for instrument nature of the measurement setup required that the pointspanel layout and are known for each car line. From remain in sets or groups of two separated laterally bythese 99% eye ellipsoid data (the 99th percentile area 15 cm (from Kemar's ear separation distance). A corn-is an ellipsoid) the 99% ear ellipsoid can be calculated, puter program was written to determine the minimumThe distances used to make this extrapolation were number of points and their locations which would betaken from the Kemar t manikin data. The manufacturer required to obtain the desired accuracy. Quite unex-claims that Kemar's dimensions represent those of a pectedly, this stability was obtainable with six points.typical person. Thus the location of 99% of the drivers' It is worthwhile to note that only one particular set ofears in any vehicle is known. This ellipsoid is used for six points proved to be successful at obtaining the de-the spatial averaging, which is required for statistical sired accuracy. This set of points and their locationsstability of the measured response, are shown in Fig. 7. The fact that these points are theIf one were to measure the spatially averaged pressure most widely separated set of points is not a coincidence.

response over the volume of the interior, the total soundpower in the vehicle could be calculated [2]. If the 3 LOCALIZED SOUND POWER METHOD

pressure is averaged over a smaller volume, the results The final procedure that was developed proved to beare proportional to a "localized sound power mea- very efficient in terms of time and personnel, whilesurement." By taking measurements over the 99% earellipsoid one can obtain the approximate sound power still yielding the required accuracy. First, the responsesat the six chosen points are measured. The averageresponse of the system that would be perceived by the response for these measurements is then computed anddriver, stored on a local storagemediumfor later use andIn order to assess the number of point measurements documentation. The delta (or difference) curves between

required to achieve a -+0.5-dB stability, the ear ellipsoid each location measurement and the average are alsowas laid out to include 18 points, as shown in Fig. 5.Not all of these points are statistically independent atthe lower frequencies, but there will still be enoughindependent measurements to work with. Fig. 4 showsthe results of these 18 measurements all plotted on thesame curve. The average response curve for these dataisshowninFig.6.The use of 18 microphone locations proved to be far

too time intensive to be useful for development work.The necessary remeasurement of the enclosure response,

_Registered trademark of Knowles Electronics, Inc.,FranklinPark, IL. Fig. 5. 18microphonemeasurementlocationsandear ellipse.

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Fig. 6. Average sound pressure levels for 6 and 18 points.

170 J. Audio Eng. Soc., Vol. 34, No. 3, 1986March

ENGINEERING REPORTS LOCALIZED SOUND POWERMETHOD

computed and stored. These delta curves are shown in etc.). A computer program was written to accomplishFig. 8. This last procedure helps to reduce the calcu- this task, thus eliminating many trial and error adjust-lations required for future tests, ments. The results of this procedure can be checkedAdditional measurements can be done without the by running another response measurement if desired.

necessity of multiple measurements. If the microphones As Fig. 10 shows, this remeasurement is not necessaryare left in the measured location, only one new mea- since the new response can be calculated directly fromsurement need be taken. The other five microphone the equalization curve. This greatly reduces the timepositions can be calculated from the previously stored required to equalize the numerous car lines produceddelta curves. The new localized sound power response by a typical automotive manufacturer.(average) can then be computed from the calculatedsix-point data. Only a single newly measured response 4 CONCLUSIONSneeds to be stored in order to recalculate the soundpower response. However, we store the entire set of It has been demonstrated that single-microphonecalculations. The validity of this approach is demon- techniques are not stable enough to be used for sound

system equalization. Further, we have shown that wide-strated in Fig. 9, where the calculated response is plottedalong with a completely remeasured and recalculated bandwidth spatially averaged sound pressure responsesset of six points, can achieve nearly any accuracy required. A methodIt is a straightforward matter to "best fit" an equal- for obtaining a very accurate acoustic frequency re-

ization curve to the response curve once it is accurately sponse curve in an automobile was outlined. The useknown. The sound system designer's goal is usually of a delta technique can reduce the time required forsubsequent measurements without sacrificing accuracy.to obtain the flattest possible system response, givena limited number of variables (center frequency, Q, These acoustic response curves can then be used for"unambiguous" sound system equalization to any de-

gree deemed feasible.

5 REFERENCES

[1] M. R. Schroeder, "The Statistical Parameters ofthe Frequency Response Curve of Large Rooms,"Acustica, vol. 4, pp. 594-600 (1954); Engl. transl.,E. R. Geddes (1981).

· [2] A. D. Pierce, Acoustics.' An Introduction to ItsPhysical Principles and Applications (McGraw-Hill,

Fig. 7. Location of final six-point measurements. New York, 1981), pp. 297-310.

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J. Audio Eng. Soc., Vol. 34, No. 3, 1986 March 171

GEDDES AND BLIND ENGINEERING REPORTS

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THEAUTHORS

L

E. Geddes H. Blind

172 J. Audio Eng. Soc., Vol. 34, No. 3, 1986 March

ENGINEERINGREPORTS LOCALIZEDSOUNDPOWERMETHOD

Earl Geddes has been experimenting with acoustics Henry Blind holds the B.S. degree in electrical andsince high school when he began studying loudspeakers, computer engineering from Wayne State University inHe obtained B.S. and M.S. degrees in physics at Eastern Detroit, MI. He was employed at the Center for In-Michigan University in 1975 and 1977, respectively, structional Technology at the university where his re-His studies included simulation theory. After graduation sponsibilities included both audio and video productionhe joined Ford Motor Company as an audio system and equipment maintenance. In addition, he also diddesign engineer. In 1980 he took an educational leave free-lance video and audio production work in the De-of absence to further study acoustics at The Pennsylvania troit area.State University where he specialized in numerical Since 1979 he has been employed at the Electricalanalysis of acoustic problems. After receiving his and Electronics Division of Ford Motor Company. AtPh.D., Dr. Geddes returned to Ford as an acoustic EED his assignments have included the design of AMtechnical specialist, an internal consultant on sound stereo decoder circuitry, electronic engine control mi-systems and noise control, croprocessor-based circuitry, and electronic compo-Dr. Geddes has been active in the AES as one of the nents engineering. For the past three years he has held

founders of the Detroit Section. He served as a section his current position as sound system design engineerofficer for four terms and was chairman of the very in the audio systems and applications engineering de-active 1984-85 term. He is presently serving as vice partment of the audio products group. His responsi-president, Central Region. He has presented numerous bilities include the design and development of futurepapers to the AES, Acoustical Society of America, sound systems for Ford Motor Company.Society of Automotive Engineers, Institute of Noise Mr. Blind is currently the chairman of the DetroitControl Engineers and the IEEE. He looks forward to Section of the Audio Engineering Society and has co-the application of new technologies in audio in which authored technical papers for both the AES and thecomputer simulation will play a key role. Society of Automotive Engineers.

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